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## C.: Overview of adaptive morphology: Trends and perspectives (2009)

Citations: | 7 - 1 self |

### Citations

1865 | Scale-space and edge detection using anisotropic diffusion
- Perona, Malik
- 1990
(Show Context)
Citation Context ...eal with improving the visual image quality by designing filters that privilege intra-region smoothing rather than inter-region smoothing. This idea motivated the introduction of nonlinear filters in =-=[20]-=- based on anisotropic diffusion. In the framework of MM, one can also consider anisotropic neighborhoods. This can be achieved via several approaches, outlined below. Most of them can be explained usi... |

500 | A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation
- Buades, Coll, et al.
(Show Context)
Citation Context ... axes are parallel to the eigendirections of the local image structure tensor. A conceptually similar adaptation based on the local Hessian was used in some morphological filters [29]. Nonlocal means =-=[2]-=- is an adaptive neighborhood filter that smooths by averaging pixels not by spatial but by graylevel proximity; it is asymptotically equivalent to (8). If we attempt to also model level-adaptive MM wi... |

166 |
Morphological image operators
- Heijmans
- 1994
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Citation Context ..., judging by the great numbers of publications that refer to adaptive algorithms. In this paper, we briefly survey the state of the art on these questions in the field of mathematical morphology (MM) =-=[12, 13, 26]-=-, which is a powerful nonlinear methodology for representing and analyzing geometrical structures in images and signals based on tools from set and lattice theory, topology and stochastic geometry, wi... |

36 |
Coherence-Enhancing Diffusion Filtering, Intl
- Weickert
- 1999
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Citation Context ...ent), whose purpose is to favor intra-region over inter-region smoothing. One could approximately interpret (8) as a linear convolution by a spatially-varying kernel. Tensor generalizations of (8) in =-=[30, 34]-=- indeed admit such an approximate interpretation as adaptive convolutions by anisotropic Gaussians whose major axes are parallel to the eigendirections of the local image structure tensor. A conceptua... |

35 |
The algebraic basis of mathematical morphology
- Ronse, Heijmans
- 1991
(Show Context)
Citation Context ..., judging by the great numbers of publications that refer to adaptive algorithms. In this paper, we briefly survey the state of the art on these questions in the field of mathematical morphology (MM) =-=[12, 13, 26]-=-, which is a powerful nonlinear methodology for representing and analyzing geometrical structures in images and signals based on tools from set and lattice theory, topology and stochastic geometry, wi... |

30 |
An adaptive morphological filter for image processing
- Cheng, Venetsanopoulos
- 1992
(Show Context)
Citation Context ...orm. Connectivity-based: Adaptivity is omnipresent in connected morphological operators [19, 25, 27], which emphasize connectivity in images instead of geodesic distances. For instance, area openings =-=[6]-=- at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the area λ of the connected components of image. The volume opening [28] at scale λ was explained in [17] as... |

25 |
A representation theory for morphological image and signal processing
- Maragos
- 1989
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Citation Context ... operator Ψ can be represented as a union of erosions by its kernel elements and as an intersection of dilations, according to Matheron’s theorem. This theory was extended to TI function operators in =-=[15]-=-, where also a basis representation was introduced for set and function operators. The above theories of TI operators were extended in [3, 4] for spatially-varying morphology by using representations ... |

25 | Mask-based second generation connectivity and attribute filters
- Ouzounis, Wilkinson
- 2007
(Show Context)
Citation Context ...ntegrating the image gradient magnitude along paths. As in [14], the geodesic time is a weighted distance transform. Connectivity-based: Adaptivity is omnipresent in connected morphological operators =-=[19, 25, 27]-=-, which emphasize connectivity in images instead of geodesic distances. For instance, area openings [6] at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the a... |

23 | Image filtering using morphological amoebas
- Lerallut, Decencière, et al.
- 2006
(Show Context)
Citation Context ...tance being chosen for its capacity to detect image edges. At least two approaches were studied in this direction: the use of a weighted graylevel distance led to the concept of morphological amoebas =-=[14]-=-. In this approach the distances are computed on a pilot image, which is a smoothed version of the original image. Another approach [10] uses a similarity measure between the image pixels that combine... |

21 |
Blosseville and F.Lenoir, “Traffic Spatial Measurements Using Video Image Processing,” David P.Casasent and Ernest L.Hall,Editors,Intelligent Robots and
- Beucher
(Show Context)
Citation Context ...or appearance. Perspectivities and other geometric deformations: One of the earliest applications that requested the use of SEs of variable size is the analysis of images from traffic control cameras =-=[1]-=-. Because of the perspective effect, vehicles at the bottom of the image are closer and appear larger than those higher in the image. Hence, the SE should follow a law of perspective, for example, var... |

17 |
Locally adaptable mathematical morphology using distance transformations
- Cuisenaire
- 2006
(Show Context)
Citation Context ...tational complexity, dramatically increasing with the size of the structuring element”, as mentioned in [11]. Thus, algorithms addressing the case of spatially adaptive SEs are still very limited. In =-=[8]-=- locally adaptable binary erosions and dilations were implemented as a variant of distance transformation algorithms. However, the only possible extension of the strategy to the graylevel case is base... |

17 | The viscous watershed transform
- Vachier, Meyer
- 2005
(Show Context)
Citation Context .... The problem is then to modify the local geometry of the image at places where regularization is required while preserving the precision of the data at places where they are accurate. This motivated =-=[18, 31]-=- to introduce level-adaptive morphological filters, associated with an adaptive SE of fixed shape and whose size adapts w.r.t. the local image intensity or contrast. These so-called viscous operators ... |

14 |
Adaptive rank order based filters
- Salembier
- 1992
(Show Context)
Citation Context ...ive Rank operators: These correspond to rank filters whose operational window is a graylevel SEM, i.e. an adaptive set of weighted signal values to be ranked. A class of adaptation rules developed in =-=[24]-=- is based on minimizing a local MSE or MAE error via steepest descent using LMS-like algorithms. These approaches weight the SE using a rank-sum arithmetic. However, in rank filters it is also possibl... |

13 |
General adaptive neighborhood image processing
- Debayle, Pinoli
(Show Context)
Citation Context ...me opening [28] at scale λ was explained in [17] as a level-adaptive connected filter (5), for which ψv equals at each intensity level v an area opening with parameter λ/v. Adaptive Neighborhoods: In =-=[5, 9]-=-, given some criterion mapping h (expressing local radiometric, morphological, or geometrical information) and a tolerance m>0, at each point x ∈ E an adaptive neighborhood V h m(x) is defined that co... |

10 |
Mathematical morphology for structures without translation symmetry
- Roerdink, Heijmans
- 1988
(Show Context)
Citation Context ...in E, is called T-invariant if ψτ = τψfor all τ ∈ T. The prototypical case is T to be the Euclidean translation group; then T-invariant means a TI operator in the classic sense. However, as stated in =-=[23]-=-, “for certain applications the use of translation-invariant transformations is not appropriate in view of an internal structure which does not possess translation symmetry”. Thus, we can restrict to ... |

9 | A PDE formulation for viscous morphological operators with extensions to intensity-adaptative operators
- Maragos, Vachier
- 2008
(Show Context)
Citation Context ...ngs [6] at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the area λ of the connected components of image. The volume opening [28] at scale λ was explained in =-=[17]-=- as a level-adaptive connected filter (5), for which ψv equals at each intensity level v an area opening with parameter λ/v. Adaptive Neighborhoods: In [5, 9], given some criterion mapping h (expressi... |

9 | Generalized flooding and multicue PDE-based image segmentation
- Sofou, Maragos
(Show Context)
Citation Context ...stances. For instance, area openings [6] at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the area λ of the connected components of image. The volume opening =-=[28]-=- at scale λ was explained in [17] as a level-adaptive connected filter (5), for which ψv equals at each intensity level v an area opening with parameter λ/v. Adaptive Neighborhoods: In [5, 9], given s... |

7 |
Affine morphology and affine signal models
- Maragos
- 1990
(Show Context)
Citation Context ... adaptive dilations). These results unify the adaptive morphological operators based on SV neighborhoods with those based on group morphology. For example, polar morphology [23] and affine morphology =-=[16]-=- were shown in [3] to correspond to SV morphological operations with specific choices for an SEM. 2.4. Level Adaptive MM A flat operator (2) uses a fixed set operator for each intensity level v; it is... |

6 |
Alternating sequential filters by adaptive-neighborhood structuring functions
- Braga-Neto
- 1996
(Show Context)
Citation Context ...me opening [28] at scale λ was explained in [17] as a level-adaptive connected filter (5), for which ψv equals at each intensity level v an area opening with parameter λ/v. Adaptive Neighborhoods: In =-=[5, 9]-=-, given some criterion mapping h (expressing local radiometric, morphological, or geometrical information) and a tolerance m>0, at each point x ∈ E an adaptive neighborhood V h m(x) is defined that co... |

5 |
Adaptative morphological operators, fast algorithms and their applications, Pattern Recognition 33
- Cheng, Venetsanopoulos
- 2000
(Show Context)
Citation Context ...nting binary adaptive morphology, an algorithm in [11] was limited to non-centered adaptive rectangles with low memory requirement and latency. In the graylevel case, a fast algorithm was proposed in =-=[7]-=- for spatially-varying SEs with adaptable shape and size based on a decomposition of the SEs in smaller 2D subelements. Tree-based fast algorithms for connected filters can be found in [19, 25]. Final... |

4 |
Adaptive morphological filters using similarities based on geodesic time
- Grazzini, Soille
- 2008
(Show Context)
Citation Context ... graylevel distance led to the concept of morphological amoebas [14]. In this approach the distances are computed on a pilot image, which is a smoothed version of the original image. Another approach =-=[10]-=- uses a similarity measure between the image pixels that combines 2242both spatial and tonal information. The similarity is defined as a decreasing function of the geodesic time, which is computed by... |

3 |
Vector-Valued Image Regularization with PDE’s
- Tschumperle, Deriche
(Show Context)
Citation Context ...ent), whose purpose is to favor intra-region over inter-region smoothing. One could approximately interpret (8) as a linear convolution by a spatially-varying kernel. Tensor generalizations of (8) in =-=[30, 34]-=- indeed admit such an approximate interpretation as adaptive convolutions by anisotropic Gaussians whose major axes are parallel to the eigendirections of the local image structure tensor. A conceptua... |

3 | News from Viscousland
- Vachier, Meyer
- 2007
(Show Context)
Citation Context ... adaptive SE of fixed shape and whose size adapts w.r.t. the local image intensity or contrast. These so-called viscous operators are no longer VTI. The viscous dilations β and erosions α proposed in =-=[32]-=- process different level sets by different scales [δr and εr denote flat dilation and erosion by a disk of radius r]: β(f) = ∨ v · δM−v[χv(f)], v α(f) = ∧ v · εM−v[χv(f)] (7) where M = sup x f(x). Som... |

1 |
Binary morphology with spatially-variant structuring elements: algorithm and architecture
- Hedberg, Dokladal, et al.
- 2008
(Show Context)
Citation Context ...tations. However, “supporting a variable structuring element shape imposes an overwhelming computational complexity, dramatically increasing with the size of the structuring element”, as mentioned in =-=[11]-=-. Thus, algorithms addressing the case of spatially adaptive SEs are still very limited. In [8] locally adaptable binary erosions and dilations were implemented as a variant of distance transformation... |

1 |
Synthesis of Adaptive Weighted Order Statistic Filters with Gradient Algorithms
- Ropert, Pele
- 1994
(Show Context)
Citation Context ...hes weight the SE using a rank-sum arithmetic. However, in rank filters it is also possible to use weights as repetition numbers of the signal values. The adaptation of such filters was approached in =-=[21]-=- by using the procedure of [24]. Viscous MM: Edge preservation is not always a goal in image processing. In many situations, e.g. in contour detection, new edges will be created in the image in order ... |

1 |
Antiextensive Connected Operators for Image and
- Salembier, Oliveras, et al.
- 1998
(Show Context)
Citation Context ...ntegrating the image gradient magnitude along paths. As in [14], the geodesic time is a weighted distance transform. Connectivity-based: Adaptivity is omnipresent in connected morphological operators =-=[19, 25, 27]-=-, which emphasize connectivity in images instead of geodesic distances. For instance, area openings [6] at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the a... |

1 |
Connectivity on
- Serra
- 1998
(Show Context)
Citation Context ...ntegrating the image gradient magnitude along paths. As in [14], the geodesic time is a weighted distance transform. Connectivity-based: Adaptivity is omnipresent in connected morphological operators =-=[19, 25, 27]-=-, which emphasize connectivity in images instead of geodesic distances. For instance, area openings [6] at scale λ are geometry-adaptive filters: the size of the structuring element is linked to the a... |

1 |
Adaptive Math. Morphology for Range Imagery
- Verly, Delanoy
- 1993
(Show Context)
Citation Context ...ting the camera at ground level and aiming towards the sky. This case requires a polar structure where the size of the structuring element increases with the distance from the center of the image. In =-=[33]-=-, the interest was in range imagery, a modality where the value of each pixel is the distance to the imaging device. Thus, the perspective requires to consider structuring elements that locally adapt ... |